Thermodynamic Constraints on Information Transmission in Quantum Ensembles

The processing of quantum information is limited by fundamental physical constraints on how information can be encoded, transmitted, and extracted. In particular, the non-orthogonality of quantum states limits their distinguishability, and thermodynamic constraints, including the energetic cost of state preparation and quantum operations, further restrict the viability of realistic information protocols. This work explores the impact of such constraints on the preparation, evolution, and readout of quantum information. We demonstrate that preparing the system for encoding and measurement affects the distinguishability and purity of the resulting ensemble of states. Furthermore, we analyze a noisy communication channel and propose an optimal protocol for encoding and decoding the transmitted information. For this realistic protocol, we show that the maximum probability of successfully retrieving the information is equal to the maximum correlation that can be achieved between the system and the register. The protocol uses only Gibbs states as free resources, ensuring minimal thermodynamic cost. Based on this, we provide a thermodynamic interpretation of the Holevo information, which quantifies the capacity of the transmitted information and establishes a fundamental limit on its retrieval in thermodynamically constrained scenarios.